How to Change the Origin when moving a Collection Instance
First Method : Set the origin in the base collection

To change the origin of a collection instance, you have to go to the object information panel, then the collections foldout and choose "set offset from cursor" with the drop-down popup on the right of the collection name.



Second Method : Set the origin in the collection instance

There is another way to do it as pointed out in the comments. Select the collection instance and type F3 to search for "Set Origin" and choose accordingly to your case. Alternatively go to Object>Set Origin. 

Note that this will be a bit more work if your object's origin is not in the center of its geometry. You can still manually place your cursor and choose "Set Origin" "From Cursor".